169.--A TANGRAM PARADOX.

The diagrams will show how the figures are constructed--each with the

seven Tangrams. It will be noticed that in both cases the head, hat, and

arm are precisely alike, and the width at the base of the body the

same. But this body contains four pieces in the first case, and in the

second design only three. The first is larger than the second by exactly

that narrow strip indicated by the dotted line between A and B. This

strip is therefore exactly equal in area to the piece forming the foot

in the other design, though when thus distributed along the side of the

body the increased dimension is not easily apparent to the eye.

[Illustration]

Amusements in Mathematics · 第 677 / 970 题